Question

An astronomical telescope has objective eyepiece of focal lengths 40 cm and 4 cm respectively. To view an object 200 cm away from the objective lens, the lenses must be separated by a distance,

• A. 46.0 cm
• B. 50.0 cm
• C. 54.0 cm
• D. 37.3 cm

Answer 1

The correct option is C 54.0 cm

Focal length of the objective lens, $f_o$ = +40 cm
Focal length of the eyepiece, $f_e$ = 4 cm
Object distance for objective lens, $u_o$ = -200 cm
Applying lens formula for objective lens,
$\frac{1}{v}$ - $\frac{1}{u}$ = $\frac{1}{f}$
$\Rightarrow$ $\frac{1}{v}$ = $\frac{1}{40}$ - $\frac{1}{200}$ = $\frac{4}{200}$
$\Rightarrow$ v = 50 cm
Image will be formed at the focus of a eyepiece lens.
So, for normal adjustment, the distance between objective and eyepiece (length of tube) will be,
v + $f_e$ = 50 + 4 = 54 cm.